Jamal is hanging up Christmas lights in his front yard to mimic the look of a Christmas tree. He starts by placing a pole in the ground and then extending strands of lights from the top of the pole to the ground in a circular pattern. The pole is 9 feet tall once placed in the ground, and each light strand is 16 feet long. If he attaches a strand of lights to the top of the pole and extends it down to the ground, what is the angle formed between the light strand and the pole?

Question

Jamal is hanging up Christmas lights in his front yard to mimic the look of a Christmas tree. He starts by placing a pole in the ground and then extending strands of lights from the top of the pole to the ground in a circular pattern. The pole is 9 feet tall once placed in the ground, and each light strand is 16 feet long. If he attaches a strand of lights to the top of the pole and extends it down to the ground, what is the angle formed between the light strand and the pole?

Answer 1

To find the angle formed between the light strand and the pole, we can use trigonometry. Let's assume the angle formed is θ.

Since the strand of lights starts at the top of the pole and extends to the ground, we have a right triangle formed. The hypotenuse of the triangle is the length of the light strand (16 feet) and the height of the triangle is the height of the pole (9 feet).

We can use the sine function to find θ:

sin(θ) = opposite/hypotenuse
sin(θ) = 9/16

We can calculate the value of sin(θ) using a calculator or a trigonometric table. Taking the inverse sine (sin^(-1)) of both sides of the equation will give us the angle θ:

θ = sin^(-1)(9/16)

Using a calculator, θ is approximately 34.98 degrees.

So, the angle formed between the light strand and the pole is approximately 34.98 degrees.